Logical analysis of the Bohr Complementarity Principle in Afshar's experiment under the NAFL interpretation

Abstract

The NAFL (non-Aristotelian finitary logic) interpretation of quantum mechanics requires that no `physical' reality can be ascribed to the wave nature of the photon. The NAFL theory QM, formalizing quantum mechanics, treats the superposed state ($S$) of a single photon taking two or more different paths at the same time as a logical contradiction that is formally unprovable in QM. Nevertheless, in a nonclassical NAFL model for QM in which the law of noncontradiction fails, $S$ has a meaningful metamathematical interpretation that the classical path information for the photon is not available. It is argued that the existence of an interference pattern does not logically amount to a proof of the self-interference of a single photon. This fact, when coupled with the temporal nature of NAFL truth, implies the logical validity of the retroactive assertion of the path information (and the logical superfluousness of the grid) in Afshar's experiment. The Bohr complementarity principle, when properly interpreted with the time dependence of logical truth taken into account, holds in Afshar's experiment. NAFL supports, but not demands, a metalogical reality for the particle nature of the photon even when the semantics of QM requires the state $S$.